Eigenvalues, Eigenspaces, Eigenbases, and the Algebraic and Geometric Multiplicity of an Eigenvalue

In this video, I define eigenspace, eigenbasis, algebraic multiplicity, and geometric multiplicity. I then work through several examples in which I find the eigenvalues of a matrix and their algebraic multiplicities. I then find the eigenspaces of the matrix corresponding to each eigenvalue, state a basis for each eigenspace, and the geometric multiplicity of each eigenvalue.